I have mixed feelings about Peter Jackson directing The Hobbit. This is coming from a die-hard LOTR fan. I own the HoME (History of Middle-Earth) books as well. I revel in my LOTR geekdom.

Important parts of the story were left out and unimportant parts were emphasized. I don’t like the scenes in which characters are not like they are described in the books. That's what bothers me the most about PJ's direction. I will admit that the films are visually stunning and I own the Extended Editions of all three yet I think Jackson fell short in some areas.
Adding to what Abimommy said ...
- I thought Glorfindel was robbed too. Arwen didn't have a role in saving Frodo's life after he was stabbed with a Morgul blade by the Nazgul. It was Glorfindel who did it. Heck, Arwen didn't have a single line of dialog in the entire LOTR story, excluding the Appendices. Introducing her as an Elven warrior-princess doesn’t work at all with the softer character Jackson tries to create in the later LOTR films.
- Aragorn's fake dying scene in the river was lame especially when you knew he was alive.
- Arwen going halfway to the Havens and turning back is also awful. She was sure about her choice of giving up mortality.
- Elves weren't at Helms Deep in Rohan. Didn't happen in any way, shape, or form. Haldir didn't die. He lived a long happy life. Ok, not sure how happy he was but he certainly wasn't killed in a melodramatic fashion by an orc.
-Beheading the Mouth of Sauron was another lame move that didn't happen
- Faramir wasn't swayed by the Ring's promise of power. He was a good man. He was created as a contrast to his brother Boromir. Faramir was to have self-control and integrity. He never took the two hobbits to Osgiliath so that he could have the Ring.
-Frodo never showed the Ring to the Nazgul on a winged steed.
- Frodo's character was changed. The scene where Gollum turns Frodo against Sam and causes him to leave was a total mutation of Frodo's character.
- Too many scenes of Arwen/Aragorn and not enough of Faramir/Eowyn. Viewers who haven't read the book would be surprised by the quick get together of Eowyn/Faramir at the end of Return of the King film since the whole section from the Houses of Healing is missing.